how to avoid gaps on the distribution of hair on a model?
Particles with Interpolated Children

Probably in some parts of your mesh, the particles (hair in this case) are not dense enough.

Interpolate option creates children based on the "main" particles properties (location, orientation...)



if these particles (main) are not enough, increasing the number of children would not help in filling the gaps. Notice how the spiral patter is similar to the one in your screenshots.

The image was made by adding a Particle system (Hair type) and tweaking the following values:


Emission Number = 100
Interpolated Display = 280


By disabling the Interplated children option, you can see the particles that actually are generated. These are the only one that will be truly affected by simulations, hair editing...the children will simply follow their properties.





You must ensure that the "main" particles are well distributed upon the mesh, and only at that point you can increase the overall density with childrens.



The image was made by adding a Particle system (Hair type) and tweaking the following values:


Emission Number = 4000
Interpolated Display = 7


Notice how the thinner part of the mesh is full of "guiding" particles.

Result: